Circles - 7th Grade Honors Math



Circles

Parts of a circle:

A circle is a set of points that are the same distance from a single point called the center.

The radius is a circle is a line segment that connects the center and one point on the circle.

A chord is a segment that connects two points on the circle.

The diameter of a circle is a chord that passes through the center.

A line that is tangent to a circle passes thought a single point on the circle and is perpendicular to a radius of the circle.

Identify the following parts of a circle:

a. Center

b. Radius

c. Chord

d. Diameter

e. Tangent

Circumference is the distance around a circle.

[pic][pic]where r is the radius

1. Find the circumference of the following circle:

a. radius of 6 feet

b. diameter of 3.5 cm

c. diameter of 45 mm

2. O is the center of a circle, C and D are points on the circle. C, O, and D are collinear. If the length of segment CD is 10 units, what is the circumference, in units, of the circle?

a. 10[pic]

b. 20[pic]

c. 25[pic]

d. 40[pic]

e. 100[pic]

3. A circular fence needs to be put up around a swimming pool. The swimming pool is 6 feet deep and 27 feet in diameter. A 3 foot tall fence is sold in 5 foot panels. How many panels should be bought in order to completely fence in the swimming pool?

a. 9 panels

b. 17 panels

c. 28 panels

d. 34 panels

4. A costume designer wants to put a white silk band around a cylinder top hat. If the radius of the cylinder part of the top hat is 4 inches, how long, in inches, should the white silk band be to just fit around the top hat?

a. 8[pic] inches

b. 25[pic] inches

c. 50[pic] inches

d. 100[pic]inches

e. 200[pic] inches

5. A bicycle has 26-inch diameter wheels. If the wheels revolved two times after the brakes were applied, the stopping distance is approximately___________. Use [pic]= 3.14

a. 37.68 feet

b. 3.14 feet

c. 163.3 feet

d. 13.6 feet

6. A vehicle travels 105.5 feet while its wheels revolve 15 times. Find the diameter of the wheels to the neatest inch. Use [pic]= 3.14. Round your answer to the nearest tenth.

a. 22.1 feet

b. 2.2 feet

c. 7.0 feet

d. 11.0 feet

7. Inside a semicircle tunnel of a diameter 30 feet, a vertical support beam is placed 8 feet from the side of a tunnel. How tall is the beam? Round off your answer to the nearest tenth.

a. 3.8 feet

b. 13.3 feet

c. 12 feet

d. 6 feet

Answers: Center C, Radius CH, CA, CD, Cord, AB, diameter AD, tangent HF, a,

1a. 12π, 1b. 3.5π, 1c. 45π, 2.A, 3. B, 4. A, 5. C, 6. B, 7. B

Area of a circle = [pic]r2

1. Find the area of a circle with circumference 20inches.

2. Find the area of the shaded region. Use [pic] = 3.14

a. 17.2 square units

b. 35.8 square units

c. 17.9 square units

d. 71.5 square units

3. The figure to the right represents the overhead view of a deck surrounding a swimming pool. What is the area of the deck?

a. 96.25[pic]square feet

b. 180.25[pic] square feet

c. 12.25[pic] square feet

d. 385[pic] square feet

4. Find the area of the shaded region.

a. 8.4[pic]

b. 5.88[pic]

c. 17.64[pic]

d. 70.56[pic]

5. The geometric figure shown below consists of a square and 4 semicircles. The diameters of the semicircles are the sides of the square, and each diameter is 10 centimeters long. Which of the following is the closest approximation of the total area, in square centimeters, of this geometric figure?

1. F. 100

2. G. 160

3. H. 260

4. J. 400

5. K. 730

6. What is the degree measure of the acute angle formed by the hands of a 12-hour clock that reads exactly 1 o’clock?

A. 15° B. 30°C. 45°D. 60°E. 72°

Answers: 1. 10/π, 2. d, 3. d, 4. b, 5. h, 6. b

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